Geometric Phases for Three State Systems

1999/02/17 by Mark Byrd, Mark S. Byrd, Byrd, Mark S. · 2 citations
Chemistry · Physics and Astronomy · #FOS: Physical sciences #Molecular spectroscopy and chirality #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #Spectroscopy and Quantum Chemical Studies #quant-ph

paper · pdf · doi:10.48550/arxiv.quant-ph/9902061

13 pages, LaTeX2e

arxiv created 1999/02/17 · openalex publication_date 1999/02/17 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The adiabatic geometric phases for general three state systems are discussed. An explicit parameterization for space of states of these systems is given. The abelian and non-abelian connection one-forms or vector potentials that would appear in a three dimensional quantum system with adiabatic characteristics are given explicitly. This is done in terms of the Euler angle parameterization of SU(3) which enables a straight-forward calculation of these quantities and its immediate generalization.

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• Twisted CP(N-1) instanton projectors and the N-level quantum density matrix
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